Host organisms with acquired immune systems reproduce, perpetuating their population. The creation of progeny hosts by a parental population introduces a generational relationship, which may be reduced to a lock-step population in which the present population is replaced by a created progeny population. This work extends the previously defined host-based population-based algorithm by introducing the generational principle. Extension of a minimal generational algorithm facilitates inter-generational information sharing inspired by maternal immunity and neo-Darwinian evolution.